Semi-sinusoidal delivery

The semi-sinusoidal delivery of the anticancer drug obeys the following equation which yields the concentration, [5-FU], as a function of time over the 24-h period ... 

In simulating the cell cycle automaton response to 5-FU, we impose a circadian profile of the anticancer medication similar to that used in clinical oncology [30, 31] 5-FU is delivered in a semi-sinusoidal manner from 10p.m. to 10a.m., with a peak at 4 a.m. (Fig. 10.3b). During the remaining hours of the day and night, the drug concentration is set to zero. For comparison, we consider similar drug delivery patterns shifted in time, with peak delivery either at 10 a.m., 4 p.m., or 10 p.m. 

It is useful to compare the circadian patterns of 5-FU delivery with the more conventional constant infusion drug-delivery pattern, in which the amount of 5-FU delivered over the 24-h period is the same as for the circadian delivery schedules. The quantity of 5-FU (Qsfu) delivered over 24 h according to the semi-sinusoidal schedule defined by Eq. (3) is given by Eq. (5) ... 

The case of the continuous infusion of 5-FU is considered in Fig. 10.5e. Because the total amount of 5-FU administered over 24 h is the same as for the circadian semi-sinusoidal patterns, the level of 5-FU - and hence the cytotoxic effect of the drug - is sometimes below and sometimes above that reached with the circadian schedule. The numerical simulations of the automaton model indicate that the cytoxicity is comparable to that observed for the most toxic circadian pattern, with peak delivery of 5-FU at 4 p.m. 

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